Universities have a reputation for being hotbeds of innovation, but they’ve never been very good at innovating in providing undergraduate education. There’s a dinosaur-like tendency to do things the way they’ve always been done.

Harold Wilson found this in the 1960s when he developed plans for a University of the Air. It was to be a different sort of university, based on distance learning, opening up undergraduate study to people who would never have otherwise had the chance. Wilson faced scathing opposition from the higher education establishment, but refused to back down. The Open University opened its doors in 1969, immediately swelling student ranks by one-fifth, and remains the UK’s largest academic institution. If universities had had their way, it wouldn’t exist.

That was the last innovation to shake up the system. Undergraduate education today remains overwhelmingly on a three-year model for just two-thirds of the year: expensive and time-inefficient for people taking time out of their career or for young people anxious to enter the workplace.

The government’s announcement last week that it wants universities to offer more two-year accelerated degrees is an old idea, but one that’s never enthused universities. What’s new is the significant financial sweetener: government has conceded that universities won’t offer two-year courses when they can make a third more by offering a three-year degree. So universities will now be allowed to charge £13,500 a year for accelerated courses.

English undergraduates already face the highest university fees in the OECD – in public institutions at least, the US Ivy League is another matter. It’s surely fair to ask whether this represents value for money, and, indeed whether £9,000 a year for a three-year degree is a fair price.

We didn’t arrive here by design, but as the result of a monumental policy cock-up. When David Willetts, then universities minister, trebled the fee cap to £9,000 in 2012, he naively thought that universities charging the maximum would be the exception, not the rule. But universities found themselves in a win-win: charging the maximum fees generated not just more revenue, but more demand in a market where students see price as a proxy for quality. Unsurprisingly, fees jumped straight up to an average of £8,600.

Universities protest that they remain hard up. In these pages last month, Chris Patten, chancellor of Oxford University, lambasted “the lamentable funding record of governments of every stripe” and universities’ “shoestring budget”. It’s a common refrain. They’ve got some gall. While every other part of the education sector is facing cuts, universities have enjoyed a 28% extra windfall in average per-student funding due to the tripling of the fee cap. Because this increase wasn’t planned, government didn’t ask for anything much extra in return.

Students and taxpayers – who are, after all, stumping up the cash – are in the dark about where this extra money is going. Universities have been incredibly resistant to any suggestion that they should be more transparent about how they spend money, even arguing for exemptions from freedom of information legislation. They have also been loath to provide comparable information about how much small group teaching, lectures and feedback the students on a particular course will receive.

Only one third of undergraduates in England think their degrees are value for money. Who could blame them? Students of history and languages report an average of just eight hours of lectures and seminars a week. Schools provide a more intensive model of education over more of the year for £4,400 a year on average, around half of what many universities charge. If a private university such as BPP can provide quality law degrees for £6,000 a year, why can’t others? It’s likely that some universities are using fees to cross-subsidise research. In others, fees will help pay for flabby management, overly generous leadership salaries and big capital investment projects, even though, in surveys, that’s not what students say they prioritise. Academic teaching staff don’t seem to be feeling the benefits: more than half in Russell Group institutions are on insecure contracts.

The standard university defence against greater transparency is that it is a world-leading sector. That’s true, but as measured by the quality of its research, not the quality of undergraduate teaching. Students are saddled with thousands of pounds of debt when they leave university. We have a duty to ask tough questions, particularly given analysis suggesting that some degrees actually carry a negative wage premium.

The government is at last trying to increase accountability for teaching in higher education from a very low base. It has developed a set of metrics that are far from perfect, but do give some sense of the quality of the academic inputs of a student’s experience. Universities will only be allowed to further increase their fees if they meet minimum benchmarks. Yes, some parts of the bill that sets this up have been clumsily drafted. But the government has shown willingness to amend the legislation to reflect concerns.

But the university response has been predictably hysterical. In criticising the university minister Jo Johnson’s decision to finally set up a regulator with some teeth, Chris Patten compared his actions to – I kid you not – Thomas Cromwell’s role in Henry VIII’s dissolution of the monasteries.

Patten argues that universities’ “autonomy and independence should be preserved at all cost”. Autonomy and independence are important, but they are not “get out of jail free” cards that can be used to dismiss altogether the need for proper accountability for universities spending of public money. A headteacher or a medical director would, rightly, never get away with the “what we do is too special to be subject to oversight” line of defence. It smacks of arrogance, complacency, and, frankly, disregard for taxpayers and students.

My challenge to universities would be: if you’re so confident that what you offer is excellent value for money, why not embrace the principles of transparency and accountability, and stop acting like you’ve something to hide?

And a note to Jo Johnson: I’d take the comparisons to Thomas Cromwell as a sign you’re ruffling the right feathers. But we could do with a bit more channelling of Harold Wilson, please.